REECE HEINLE CP 3.pdf - Computing Project 2 Reece Heinle Beam analysis Introduction Computing Project number 3 is different form the computing projects

REECE HEINLE CP 3.pdf - Computing Project 2 Reece Heinle...

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Computing Project 2- Reece Heinle Beam analysis Introduction: Computing Project number 3 is different form the computing projects before it. The project has a large focus on modeling the figures (including a three-dimensional model), as well as calculating large sums of numbers in forms of magnitudes, directions, and unit vectors as per usual. The objectives of the problem are modeled as follows. Part one requires the modeling of two trusses in a plot diagram (divided into subsection a, and b), as well as a presentation of all the individual unit vectors and nodal joints in the trusses respectively. Subsection a contains the programming to completely model a two-dimensional diagram of any truss, provided the user could input the positions of each of the nodes, as well as specify which nodes are connected in the array. Subsection b does largely the same calculations as subsection a, except the figure of subsection b has a capacity to create 3-d models that can be observed and rotated in the MATLAB interface. Theoretically, any 2d or 3d trusses can be modeled in this program, provided the user knows the position vectors and connections for each node. Part two of the code has similar end goals to part one, the truss must be modeled, nodes must be listed, and unit vectors must be calculated. However, this part of the program does not require as much user input as the last section. This code simply requires a radius and number of nodes, and automatically creates an interconnected array of nodes in the formation of a semi-circle. Theory: The first, and perhaps most important theory involved in this specific project, are all of those that have to do with matrices. Matrix multiplication, normalization, and addition were all essential to the completion of this code. Normalization is heavily involved in the process of creating a unit vector. Let’s suppose we have a particular vector connecting two points in space A, and B where. ? = 4? 1 + 3? 2 − 5? 3 ? = 0? 1 + 0? 2 = 0? 3 To find the vector connecting A and B, B must be subtracted from A. In this case, B is at the origin so, ?? = 4𝐞 ? + 3𝐞 ? − 5𝐞 ? AB is a vector connecting the two dots with specified directions in e1 e2 and e3. This is great, but in order to calculate forces on trusses, unit vectors are an essential piece. A unit vector is simply a normalized vector, or a vector divided by its magnitude. This means a unit vector is a vector identical in direction to the original, with a magnitude of 1 for simpler calculations. To calculate the magnitude of the vector (or normalize the vector), each dimension (in e1 e2 and e3)